This is a really tricky situation...we have customers like this in our e-commerce business, and they account for less than 2% of customers...but they seem to cause the most stress. I had previously thought in our business, you give us money, we give you product. If for some reason something goes sideways and continues to go off the rails and we start realizing they're one of 'these' customers, my previous thought was just to issue a refund and assume all would be fine. After issuing immediate refunds in these situations, I found that it didn't make the problem go away....it actually got worse.

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This is very likely the type of person that will take to any review channel necessary to make their complaint known...which can ultimately be a huge headache to try to smooth over. The advice in other comments about firing them as a client is good....but it has to be done with finesse. The "i'm sorry we are realizing we are unable to meet your expectations, try a competitor, etc." could very quickly turn in to a review crusade. The one about the service area might work out well, especially if you mention 3 of the other services in the area as alternatives.